Dimensions, embeddings, and attractors

>> Google Books

所蔵情報QRコード

Dimensions, embeddings, and attractors / James C. Robinson

資料種別:: 図書
出版情報:: Cambridge : Cambridge University Press, 2011
形態:: xii, 205 p. ; 24 cm
シリーズ名:: Cambridge tracts in mathematics ; 186 <BA00134372>
著者名:: Robinson, James C., 1969- <DA13100460>
ISBN:: 9780521898058 [0521898056] (: hardback)
書誌ID:: BB04267626

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references (p. 196-201) and index

主題:

MATHEMATICS / General bisacsh

言語:

英語

目次情報:

Preface

Introduction

Finite-Dimensional Sets / Part I：

Lebesgue covering dimension / 1：

Covering dimension / 1.1：

The covering dimension of In / 1.2：

Embedding sets with finite covering dimension / 1.3：

Large and small inductive dimensions / 1.4：

Exercises

Hausdorff measure and Hausdorff dimension / 2：

Hausdorff measure and Lebesgue measure / 2.1：

Hausdorff dimension / 2.2：

The Hausdorff dimension of products / 2.3：

Hausdorff dimension and covering dimension / 2.4：

Box-counting dimension / 3：

The definition of the box-counting dimension / 3.1：

Basic properties of the box-counting dimension / 3.2：

Box-counting dimension of products / 3.3：

Orthogonal sequences / 3.4：

An embedding theorem for subsets of R^N in terms of the upper box-counting dimension / 4：

Prevalence, probe spaces, and a crucial inequality / 5：

Prevalence / 5.1：

Measures based on sequences of linear subspaces / 5.2：

Embedding sets with d_H (X - X) finite / 6：

No linear embedding is possible when d_H (X) is finite / 6.1：

No modulus of continuity is possible for L^-1 / 6.2：

Thickness exponents / 7：

The thickness exponent / 7.1：

Lipschitz deviation / 7.2：

Dual thickness / 7.3：

Embedding sets of finite box-counting dimension / Exercises：

Embedding sets with Hölder continuous parametrisation / 8.1：

Sharpness of the Hölder exponent / 8.2：

Assouad dimension / 9：

Homogeneous spaces and the Assouad dimension / 9.1：

Assouad dimension and products / 9.2：

Homogeneity is not sufficient for a bi-Lipschitz embedding / 9.3：

Almost bi-Lipschitz embeddings / 9.5：

Sharpness of the logarithmic exponent / 9.6：

Consequences for embedding compact metric spaces / 9.7：

Finite-Dimentional Attractors / Part II：

Partial differential equations and nonlinear semigroups / 10：

Nonlinear semigroups and attractors / 10.1：

Sobolev spaces and fractional power spaces / 10.2：

Abstract semilinear parabolic equations / 10.3：

The two-dimensional Navier-Stokes equations / 10.4：

Attracting sets in infinite-dimensional systems / 11：

Global attractors / 11.1：

Existence of the global attractor / 11.2：

Example 1: semilinear parabolic equations / 11.3：

Example 2: the two-dimensional Navier-Stokes equations / 11.4：

Bounding the box-counting dimension of attractors / 12：

Coverings of T[B(0,1)] via finite-dimensional approximations / 12.1：

A dimension bound when Df ∈ L_λ/2 (B), λ < 1/2 / 12.2：

Finite dimension when Df ∈ L₁ (X) / 12.3：

Semilinear parabolic equations in Hilbert spaces / 12.4：

Thickness exponents of attractors / 13：

Zero thickness / 13.1：

Zero Lipschitz deviation / 13.2：

The Takens Time-Delay Embedding Theorem / 14：

The finite-dimensional case / 14.1：

Periodic orbits and the Lipschitz constant for ordinary differential equations / 14.2：

The infinite-dimensional case / 14.3：

Periodic orbits and the Lipschitz constant for semilinear parabolic equations / 14.4：

Parametrisation of attractors via point values / 15：

Real analytic functions and the order of vanishing / 15.1：

Dimension and thickness of A in C^r (Ω, R^d) / 15.2：

Proof of Theorem 15.1 / 15.3：

Applications / 15.4：

Solutions to exercises

References

Index

Preface

Introduction

Finite-Dimensional Sets / Part I：

Lebesgue covering dimension / 1：

Covering dimension / 1.1：

The covering dimension of In / 1.2：

続きを見る

東工大ブックレビュー

類似資料:

1 図書 Infinite-dimensional dynamical systems : an introduction to dissipative parabolic PDEs and the theory of global attractors (: pbk) Robinson, James C., 1969- Cambridge University Press	7 図書 From finite to infinite dimensional dynamical systems (: hard ; : pbk) Robinson, James C. (James Cooper), 1969-, Glendinning, Paul, North Atlantic Treaty Organization. Scientific Affairs … Kluwer Academic Publishers
2 電子ブック Attractors for infinite-dimensional non-autonomous dynamical systems Carvalho, Alexandre, Carvalho, Alexandre N., Langa, José A., Robinson, James SpringerLink Books - AutoHoldings, Springer New York	8 電子ブック The Structure of Attractors in Dynamical Systems Nelson G. Markley, Martin, J. C., Perrizo, W. SpringerLink Books - AutoHoldings, Springer Berlin Heidelberg
3 図書 Partial differential equations in fluid mechanics (: pbk) Fefferman, Charles, 1949-, Robinson, James C., 1969-, Rodrigo, Jose L. Cambridge University Press	9 電子ブック Mathematical Analysis of the Navier-Stokes Equations: Cetraro, Italy 2017 Hieber, Galdi, Giovanni P., Robinson, James C., Shibata, Yoshihiro SpringerLink Books - AutoHoldings, Springer International Publishing
4 電子ブック Partial differential equations in fluid mechanics Fefferman, Charles, 1949-, Robinson, James C., 1969-, Rodrigo, Jose L. Cambridge University Press	10 図書 Analysis in integer and fractional dimensions (: hbk.) Blei, R. C. (Ron C.) Cambridge University Press
5 図書 Advanced mathematics for applications (: hbk ; : pbk) Prosperetti, Andrea Cambridge University Press	11 図書 Undergraduate instrumental analysis Robinson, James W., 1923- M. Dekker
6 図書 Origami 5 : Fifth International Meeting of Origami Science, Mathematics, and Education (: pbk) International Meeting of Origami Science, Mathematics, and Education, Wang-Iverson, Patsy, Lang, Robert J., Yim, Mark CRC Press	12 図書 Atomic absorption spectroscopy Robinson, James W., 1923- M. Dekker